cp's OEIS Frontend

A109198 Minimal value of k > 0 such that n^3 + k^2 is semiprime.

%I A109198 #11 Mar 04 2018 03:07:00
%S A109198 2,3,1,8,1,2,1,8,5,4,9,4,11,2,13,2,1,12,1,12,7,5,1,2,5,3,3,10,1,18,7,
%T A109198 4,3,2,5,2,7,2,7,2,7,6,1,2,5,7,3,4,11,2,3,16,5,2,11,2,9,2,1,40,1,4,5,
%U A109198 8,5,9,17,2,7,5,1,6,1,4,3,14,3,4,1,18,9,10,3,6,5,3,15,4,9,3,7,10,11,2,3,12
%N A109198 Minimal value of k > 0 such that n^3 + k^2 is semiprime.
%C A109198 When n+1 and n^2+1 are both prime, then k=1.
%F A109198 a(n) = minimal value of k > 0 such that n^3 + k^2 is semiprime.
%e A109198 a(0) = 2 because 0^3 + 1^2 = 1 is not semiprime, but 0^3 + 2^2 = 4 = 2^2 is.
%e A109198 a(1) = 3 because 1^3 + 1^2 and 1^3 + 2^2 are not semiprime, but 1^3 + 3^2 = 10 = 2 * 5 is semiprime.
%e A109198 a(59) = 40 because 59^3 + 40^2 = 206979 = 3 * 68993 and for no smaller k > 0 is 59^3 + k^2 a semiprime.
%e A109198 a(100) = 1 because 100^3 + 1^2 = 1000001 = 101 * 9901.
%t A109198 k2sp[n_]:=Module[{n3=n^3,k=1},While[PrimeOmega[n3+k^2]!=2,k++];k]; Array[ k2sp,100,0] (* _Harvey P. Dale_, Oct 15 2013 *)
%o A109198 (PARI) A109198(n)={local(r);r=1;while(bigomega(n^3+r^2)<>2,r=r+1);r} \\ _Michael B. Porter_, May 14 2010
%Y A109198 Cf. A001358, A108714, A109197.
%K A109198 easy,nonn
%O A109198 0,1
%A A109198 _Jonathan Vos Post_, Jun 22 2005